The geometric average annual return for a large capitalization stock portfolio is 12% for ten years and 5% per year for the next five years.The geometric average annual return for the entire 15-year period is:

Question

Quizplus · Accepted Answer

The geometric average return formula for multi-year periods is:
(1 + g)^n = (1 + r1)(1 + r2) ...(1 + rn)
where g is the geometric average return, and r1, r2, ..., rn are the annual returns over n years.

To find the geometric average return for a 15-year period:
(1 + g)^15 = (1 + 0.12)^10 (1 + 0.05)^5
(1 + g)^15 = 3.10532
1 + g = 1.0911
g = 0.0911 or 9.11%

Therefore, the answer is B, with a geometric average return of 9.62%.

The Geometric Average Annual Return for a Large Capitalization Stock